1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various nations and other regions \(m\) of United Kingdom. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was c62ef5b7f851ac4b58c3379b5c71b76a3e9e50b5.

2 Data

Data is obtained [3]. This contains the daily cases, hospital admissions and deaths for United Kingdom by various geographies. Here the data is accessed by specimen date, admission date and date of death.

Once history is built up an allowance for rate reported cases, admissions and deaths will be made. For now the data is cut-off a week prior to the last case date in the data. All data prior to 1 March 2020 are removed.

3 Methodology

The methodology is described in detail here.

4 Results by Nation

4.1 Cases

Below we plot cumulative case count on a log scale by nation:

Cumulative Cases by Nation

Cumulative Cases by Nation

4.2 Admissions

Below we plot cumulative hospital admissions on a log scale.

Cumulative Admissions by Nation

Cumulative Admissions by Nation

4.3 Deaths

Below we plot the cumulative deaths by nation on a log scale:

Cumulative Deaths by Nation

Cumulative Deaths by Nation

4.4 Current \(R_{t,m}\) estimates by Nation

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Nation
Nation Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
England cases 280,648 2021-01-15 0.8 0.8 0.9
England admissions 26,130 2021-01-15 1.0 1.0 1.0
England deaths 6,790 2021-01-15 1.1 1.2 1.2
Northern Ireland cases 7,240 2021-01-15 0.7 0.7 0.8
Northern Ireland admissions 625 2021-01-15 0.9 1.0 1.1
Northern Ireland deaths 145 2021-01-15 1.2 1.4 1.7
Scotland cases 11,910 2021-01-15 0.8 0.8 0.8
Scotland admissions 1,216 2021-01-15 0.9 1.0 1.1
Scotland deaths 347 2021-01-15 1.0 1.2 1.3
Wales cases 9,623 2021-01-15 0.7 0.8 0.8
Wales admissions 841 2021-01-15 0.9 0.9 1.0
Wales deaths 290 2021-01-15 0.9 1.0 1.1
Estimated Effective Reproduction Number by Nation

Estimated Effective Reproduction Number by Nation

4.5 Maps of Effective Reproduction Number

Below we plot the current effective reproduction number on maps with boundaries provided by [4].

4.5.1 Cases

4.5.2 Admissions

4.5.3 Deaths

4.6 Graphs over Time

Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.

4.6.1 England

4.6.2 Northern Ireland

4.6.3 Scotland

4.6.4 Wales

5 Results by Region

5.1 Cases

Below we plot cumulative case count on a log scale by region:

Cumulative Cases by Region

Cumulative Cases by Region

5.2 Deaths

Below we plot the cumulative deaths by region on a log scale:

Cumulative Deaths by Region

Cumulative Deaths by Region

5.3 Current \(R_{t,m}\) estimates by Region

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Region
Region Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Northern Ireland cases 7,240 2021-01-15 0.7 0.7 0.8
Northern Ireland deaths 145 2021-01-15 1.2 1.4 1.7
Scotland cases 11,910 2021-01-15 0.8 0.8 0.8
Scotland deaths 347 2021-01-15 1.0 1.2 1.3
Wales cases 9,623 2021-01-15 0.7 0.8 0.8
Wales deaths 290 2021-01-15 0.9 1.0 1.1
East Midlands cases 19,579 2021-01-15 0.9 0.9 0.9
East Midlands deaths 545 2021-01-15 1.2 1.3 1.4
East of England cases 33,031 2021-01-15 0.8 0.8 0.8
East of England deaths 1,111 2021-01-15 1.1 1.2 1.3
London cases 63,542 2021-01-15 0.7 0.8 0.8
London deaths 1,186 2021-01-15 1.0 1.1 1.1
North East cases 8,981 2021-01-15 0.8 0.9 0.9
North East deaths 248 2021-01-15 1.0 1.2 1.3
North West cases 38,995 2021-01-15 0.9 0.9 0.9
North West deaths 701 2021-01-15 1.1 1.2 1.3
South East cases 46,463 2021-01-15 0.8 0.8 0.8
South East deaths 1,431 2021-01-15 1.1 1.2 1.2
South West cases 19,410 2021-01-15 0.9 0.9 0.9
South West deaths 418 2021-01-15 1.2 1.3 1.5
West Midlands cases 34,119 2021-01-15 0.9 1.0 1.0
West Midlands deaths 711 2021-01-15 1.1 1.2 1.3
Yorkshire and The Humber cases 14,352 2021-01-15 0.8 0.8 0.9
Yorkshire and The Humber deaths 341 2021-01-15 0.9 1.0 1.1
Estimated Effective Reproduction Number by Region

Estimated Effective Reproduction Number by Region

5.4 Maps of Effective Reproduction Number

Below we plot the current effective reproduction number on maps with boundaries provided by [5].

5.4.1 Cases

5.4.2 Deaths

5.5 Graphs over Time

Below we plot results for each nation.

5.5.1 Northern Ireland

5.5.2 Scotland

5.5.3 Wales

5.5.4 East Midlands

5.5.5 East of England

5.5.6 London

5.5.7 North East

5.5.8 North West

5.5.9 South East

5.5.10 South West

5.5.11 West Midlands

5.5.12 Yorkshire and The Humber

6 Results by NHS Region

6.1 Current \(R_{t,m}\) estimates by Region

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Region
Region Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Northern Ireland admissions 625 2021-01-15 0.9 1.0 1.1
Scotland admissions 1,216 2021-01-15 0.9 1.0 1.1
Wales admissions 841 2021-01-15 0.9 0.9 1.0
East of England admissions 3,173 2021-01-15 0.9 1.0 1.0
London admissions 5,473 2021-01-15 0.9 0.9 1.0
North West admissions 3,095 2021-01-15 1.1 1.1 1.2
South East admissions 4,152 2021-01-15 0.9 0.9 1.0
South West admissions 2,108 2021-01-15 1.1 1.2 1.3
Midlands admissions 5,122 2021-01-15 1.1 1.1 1.2
North East and Yorkshire admissions 3,007 2021-01-15 1.0 1.1 1.1
Estimated Effective Reproduction Number by Region

Estimated Effective Reproduction Number by Region

6.2 Maps of Effective Reproduction Number

Below we plot the current effective reproduction number on maps with boundaries provided by [6].

6.3 Graphs over Time

Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.

6.3.1 East of England

6.3.2 London

6.3.3 Midlands

6.3.4 North East and Yorkshire

6.3.5 North West

6.3.6 South East

6.3.7 South West

7 Results by Upper Tier Local Authority

7.1 Highest \(R_{t,m}\) as estimated using cases

Below we plot Upper Tier Local Authorities with the highest reproduction numbers (providing they had at least 100 cases in last 7 days):

## Selecting by Rt_ui_95
Estimated Effective Reproduction Number by Upper Tier Local Authority
Upper Tier Local Authority Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Gwynedd cases 258 2021-01-15 1.1 1.2 1.4
Plymouth cases 865 2021-01-15 1.0 1.1 1.2
Clackmannanshire cases 137 2021-01-15 0.9 1.1 1.3
Shropshire cases 1,449 2021-01-15 1.0 1.0 1.1
Bolton cases 1,126 2021-01-15 1.0 1.0 1.1
Solihull cases 1,142 2021-01-15 1.0 1.0 1.1
Newcastle upon Tyne cases 855 2021-01-15 1.0 1.0 1.1
Peterborough cases 1,102 2021-01-15 1.0 1.0 1.1
Derby cases 1,730 2021-01-15 1.0 1.0 1.1
St. Helens cases 1,489 2021-01-15 1.0 1.0 1.1
Leicestershire cases 2,532 2021-01-15 1.0 1.0 1.1
Dudley cases 2,159 2021-01-15 1.0 1.0 1.1
Ceredigion cases 115 2021-01-15 0.8 1.0 1.2
North Somerset cases 861 2021-01-15 0.9 1.0 1.1
Torbay cases 337 2021-01-15 0.9 1.0 1.1
Blackpool cases 431 2021-01-15 0.9 1.0 1.1
Bath and North East Somerset cases 741 2021-01-15 0.9 1.0 1.0
Powys cases 262 2021-01-15 0.9 1.0 1.1
Barnsley cases 579 2021-01-15 0.9 1.0 1.0
Isle of Anglesey cases 107 2021-01-15 0.8 1.0 1.1
West Lothian cases 270 2021-01-15 0.8 0.9 1.0
South Ayrshire cases 262 2021-01-15 0.8 0.9 1.1
Rutland cases 95 2021-01-15 0.7 0.9 1.1
East Lothian cases 121 2021-01-15 0.8 0.9 1.1
Argyll and Bute cases 67 2021-01-15 0.7 0.9 1.1

7.2 Risk Quadrants

The plots below show weekly cases (or deaths) on the X-axis and the reproduction number on the Y-axis. By dividing this into 4 quadrants we can identify upper tier local authorities with high cases and high reproduction numbers, or high cases and low reproduction numbers etc.

Values where the reproduction number exceeds 3 are plotted at 3.

7.2.1 Cases

Risk Quadrants - Cases

7.2.2 Deaths

Risk Quadrants - Deaths

7.3 Map of Effective Reproduction Number (Cases)

Below we plot the current effective reproduction number estimated from case data on maps with boundaries provided by [7].

7.4 Map of Reproduction Number by Upper Tier Local Authority Over 60 days

Below the reproduction number by week for each Upper Tier Local Authority is animated over last 60 days:

8 Detailed Results

Detailed output are saved to a comma-separated value file. The file can be found here.

9 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths. It may well be that some catch-up in reported deaths is exaggerating the estimates for October.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

10 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

11 Digital boundaries

Office for National Statistics licensed under the Open Government Licence v.3.0

Contains OS data © Crown copyright and database right 2020

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] Office for National Statistics, “Official UK Coronavirus Dashboard,” 2020. [Online]. Available: https://coronavirus.data.gov.uk. [Accessed: 07-Nov-2020]

[4] Office for National Statistics, “Countries (December 2019) Boundaries UK BUC,” 09-Oct-2017. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]

[5] Office for National Statistics, “NUTS Level 1 (January 2018) Ultra Generalised Clipped Boundaries in the United Kingdom,” 31-Jul-2017. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/nuts-level-1-january-2018-ultra-generalised-clipped-boundaries-in-the-united-kingdom. [Accessed: 07-Nov-2020]

[6] Office for National Statistics, “NHS England Regions (April 2020) Boundaries EN BUC,” 13-May-2020. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]

[7] Office for National Statistics, “Counties and Unitary Authorities (December 2019) Boundaries UK BUC,” 11-Mar-2020. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/counties-and-unitary-authorities-december-2019-boundaries-uk-buc. [Accessed: 07-Nov-2020]